derivative of sqrt(x)(x^2-1)

Lösung

\frac{d}{d x} (x (x^{2} - 1))

\frac{5 x ^{2} - 1}{2 x}

Schritte zur Lösung

\frac{d}{d x} (x (x^{2} - 1))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x^{2} - 1

= \frac{d}{d x} (x) (x^{2} - 1) + \frac{d}{d x} (x^{2} - 1) x

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} (x^{2} - 1) = 2 x

= \frac{1}{2 x} (x^{2} - 1) + 2 x x

Vereinfache

\frac{1}{2 x} (x^{2} - 1) + 2 x x : \frac{5 x ^{2} - 1}{2 x}

= \frac{5 x ^{2} - 1}{2 x}

\frac{d}{d x} ((x + 2)^{2} \cdot \frac{x ^{2}}{2})

\frac{d}{d x} (\frac{e ^{x}}{5 x ^{3}})

t an g e n t f (x) = (1 + 5 x)^{12}, (0, 1)

10 y^{^{'}} = 10 \cdot 9.81 - 5 y

t an g e n t y = \frac{1}{x - 1}, at x = 6